Question

i need help with question 36 and the graph attached, make sure to read the information at the top of the graph

Answer 1

The given system of inequalities is

`\begin{gathered} x+2y>6\rightarrow(1) \\ -2x+3y\leq6\rightarrow(2) \end{gathered}`

At first, we will draw each line using 2 points on it

Remember:

1. If the sign of inequality has equal, then the line must be solid

2. If the sign of inequality has no equal sign, then the line is dashed

3. If the sign of inequality is >, then the shaded area is above the line

4. If the sign of inequality is <, then the shaded area is under the line

Now, let us find the points on the lines

`\begin{gathered} x+2y=6 \\ x=0 \\ 0+2y=6 \\ 2y=6 \\ (2y)/(2)=(6)/(2) \\ y=3 \\ 1st\rightarrow(0,3) \end{gathered}`
`\begin{gathered} x+2y=6 \\ y=0 \\ x+2(0)=6 \\ x+0=6 \\ x=6 \\ 2nd\rightarrow(6,0) \end{gathered}`

We will do the same with the second line

`\begin{gathered} -2x+3y=6 \\ x=0 \\ -2(0)+3y=6 \\ 0+3y=6 \\ (3y)/(3)=(6)/(3) \\ y=2 \\ 1st\rightarrow(0,2) \end{gathered}`
`\begin{gathered} -2x+3y=6 \\ y=0 \\ -2x+3(0)=6 \\ -2x+0=6 \\ -2x=6 \\ (-2x)/(-2)=(6)/(-2) \\ x=-3 \\ 2nd\rightarrow(-3,0) \end{gathered}`

We will draw the graph using the points above

The red graph represents inequality (1)

The red line is dashed

The shaded area is above the line

The blue graph represents the inequality (2)

The blue line is solid

The shaded area is below the line

The area of the solution is the area that contains the two colors together

The area of the solution is marked by a star.